Combined Level-Set-XFEM-Density Topology Optimization for Large Deformation in 4D Printed Structures

Abstract

Design tools that take advantage of the growing fabrication flexibility are becoming more and more necessary as 
additive manufacturing advances. With a precision of tens of microns, multi-material 3D printing enables the creation 
of components from several materials with distinct mechanical, thermal, and "active" behaviors that may be organized 
spatially in three dimensions. Shape-changing characteristics may be included into additively built structures by 
taking advantage of this. 4D printing is 3D printing that changes its form downstream in reaction to an environmental 
input like light, humidity, or temperature. In order to produce active structures that experience significant deformation 
and assume a desirable target displacement upon heat activation, a design technique for determining the material 
layout of 4D printed materials with internal, programmable stresses is presented in this study. The dynamic multi-
material design issue is described in the optimization process by combining density-based topology optimization with 
a level set approach and the extended finite element method (XFEM). To precisely forecast the behavior of nonlinear 
slender structures throughout the design development, a higher-order XFEM method is combined with a finite 
deformation hyperelastic thermomechanical model. The special capabilities of the suggested framework are shown 
using examples. When 4D printed physical specimens and numerical predictions of optimum shape-changing 
structures are compared, excellent agreement is found. All things considered, a methodical design strategy that 
produces non-intuitive material layouts and geometries to accomplish goal deformations of varying complexity is 
described for the creation of 4D printed active structures with geometrically nonlinear behavior